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A '''sublinear''' function (or functional, as is more often used in functional analysis), in linear algebra and related areas of mathematics, is a function f: V \rightarrow \mathbf{F} on a vector space ''V'' over '''F''', an ordered field (e.g. the real numbers \mathbb{R}), which satisfies :f(\gamma x ) = \gamma f\left( x\right)   for any positive \gamma\in \mathbf{F} and any ''x'' ∈ ''V'' (''positive homogeneity''), and f(x + y) \le f(x) + f(y)  for any ''x'', ''y'' ∈ ''V'' (subadditivity). In functional analysis the name '''Banach functional (mathematics)|functional''' is used for sublinear function, especially when formulating Hahn–Banach theorem. In computer science, a function f: \mathbb{Z^+} \rightarrow \mathbb{R} is called sublinear if f(n) \in o(n) in Big O notation|asymptotic notation (Notice the small \,o). Formally, f(n) \in o(n) if and only if, for any given \,c > 0, there...
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